Club does not imply the existence of a Suslin tree

Suslin树的保持与闭无界同构

Suslin tree preservation and club isomorphisms

本文构造了存在Suslin树且特定正规Aronszajn树闭无界同构的集合论模型，还证明自由正规Suslin树经c.c.c.力迫可实现n-自由且高维导出树特殊的结果。

Club isomorphisms on higher Aronszajn trees

We prove the consistency, assuming an ineffable cardinal, that any two normal countably closed $ω_2$-Aronszajn trees are club isomorphic. This work generalizes to higher cardinals the property of Abraham-Shelah that any two normal $ω_1$-Aronszajn trees are club isomorphic, which follows from $\textsf{PFA}$. The statement that any two normal countably closed $ω_2$-Aronszajn trees are club isomorphic implies that there are no $ω_2$-Suslin trees, so our proof also expands on the method of Laver-Shelah for obtaining the $ω_2$-Suslin hypothesis.

PFA($T^*$) 的新推论

New consequences of PFA($T^*$)

本文扩展了力迫公理 PFA($T^*$) 的推论列表，证明其蕴含映射反射原理（MRP）和开放图公理（OGA），并揭示了特殊 Aronszajn 树与几乎 Suslin 树在 club-同构性上的不同表现。

μ ^+上的μ-完全Suslin树

mu-complete Suslin trees on mu^+

我们证明了mu = mu^{< mu}，2 ^mu = mu^+和"存在一个由共尾性<mu的序数组成的mu^+的非反射平稳子集“暗示着在mu^+上存在一棵mu-完全Souslin树。

A model with Suslin trees but no minimal uncountable linear orders other than $ω_1$ and $-ω_1$

We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $ω_1$ and $-ω_1$, answering a question of J. Baumgartner. This is done by a Jensen-type iteration, proving that one can force CH together with a restricted form of ladder system uniformization on trees, all while preserving a rigid Suslin tree.

Guessing models, trees, and cardinal arithmetic

Since being isolated by Viale and Weiss in 2009, the Guessing Model Property has emerged as a particularly prominent and powerful consequence of the Proper Forcing Axiom. In this paper, we investigate connections between variations of the Guessing Model Property and cardinal arithmetic, broadly construed. We improve upon results of Viale and Krueger by proving that a weakening of the Guessing Model Property implies Shelah's Strong Hypothesis. We also prove that, though the Guessing Model Property is known not to put an upper bound on the size of the continuum, it does imply that $2^{ω_1}$ is a…